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Mathematical modeling of electrorheological materials. (English) Zbl 0971.76100

Summary: We derive governing equations for the motion of electrorheological fluids, where the complex interactions between the thermo-mechanical and electromagnetic fields are taken into account. Starting point are the general balance laws of thermodynamics and electrodynamics. Based on simplifications which reflect the nature of electrorheological fluids, and on a non-dimensionalization taking into account typical situations in applications, we obtain the final set of equations which is also tractable for mathematical and numerical analysis. Finally, we discuss the consequences of the second law of thermodynamics for various special constitutive relations for Cauchy stress tensor.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
80A17 Thermodynamics of continua
78A25 Electromagnetic theory (general)
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